How to change repeating decimal to fraction... but with a number at the start that does not repeat... Ex: .7222222?
回答 (5)
2016-08-03 8:10 pm
✔ 最佳答案
0.7222...The repeat pattern is 2.
Let x = 0.7222...
Multiply x by 10, so the first repeat is immediately to the right of the decimal point:
10x = 7.222...
Multiply x by 100, so the first repeat is immediately to the left of the decimal point:
100x = 72.222...
100x-10x = 72.222... - 7.222...
90x = 65
x = 65/90 = 13/18
2016-08-03 7:49 pm
0.7222222222.....
All you really need to concern yourself with is the repeating digits, and mainly how often they repeat. For instance, the block of 22222222 repeats with every digit
x = 0.722222222......
10x = 7.222222222.....
10x - x = 7.2222222.... - 0.72222222.....
10x - x = 7.2 - 0.7
9x = 6.5
18x = 13
x = 13/18
All you really need to concern yourself with is the repeating digits, and mainly how often they repeat. For instance, the block of 22222222 repeats with every digit
x = 0.722222222......
10x = 7.222222222.....
10x - x = 7.2222222.... - 0.72222222.....
10x - x = 7.2 - 0.7
9x = 6.5
18x = 13
x = 13/18
2016-08-03 7:49 pm
n = 0.72222.....then 10 n = 7.222....---> 9n = 6.5---> n = 65 / 90
2016-08-03 7:47 pm
Assuming the 2's repeat forever, i.e.:
x = 0.7222222222222222...
10x = 7.22222222222222...
Subtract those:
9x = 6.5
x = 6.5/9
x = 17/18
x = 0.7222222222222222...
10x = 7.22222222222222...
Subtract those:
9x = 6.5
x = 6.5/9
x = 17/18
2016-08-03 9:02 pm
Let P = 0.72222..
Hence
100P = 72.2222...
Subtract
99P = 71.5
P = 71.5 / 99 = > (143/2) / 99 = 143/198 = 13/18
Hence
100P = 72.2222...
Subtract
99P = 71.5
P = 71.5 / 99 = > (143/2) / 99 = 143/198 = 13/18
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